The geometry of the contact lens surface that rests on the cornea, also called back or concave lens surface and opposite to the front or convex surface, is normally identified by predefined geometrical parameters.
Contact lenses can be grouped in two classes, depending on the shape of the back surface which matches the cornea: spherical and aspherical.
Spherical geometry is obtained from combined spherical surfaces centered on the symmetry axis of the lens. Such surfaces are identified by the radius of the corresponding sphere and their radial extension about the symmetry axis of the lens.
The use of corneal topography in contact lens fitting has been suggested applied to spherical geometry to evaluate the base curve radius of a contact lens. See for references Chapter 4 of "Contact Lenses, the CLAO Guide to Basic Science and Clinical Practice", by the Contact Lens Association of Ophthalmologists, Grune & Stratton, Orlando, Fla., 1984.
Lenses having more complex rotation surfaces, such as having a conic curve profile, polynomial or other, are generically called aspherical. Toric or other shapes without rotational symmetry are built as variants of the previous ones.
Spherical lenses are often uncomfortable, and their geometry often has a too low number of degrees of freedom to match the large variability of corneal morphology.
Aspherical geometry has been introduced in the contact lens field when technology allowed their manufacturing with sufficient accuracy, with the aim of matching more varieties of corneal topologies.
On the other hand, the high number of degrees of freedom of the aspherical lenses in an inconvenience for the contact lens specialist who has to consider many parameters (e.g. polynomial coefficients) and cannot obtain the final lens shape without several fitting tries that may require several lens manufactured, loss of time, higher costs and unease for the patient and the fitter.
In the case of sclera support lenses molding resin or rubber are used to reproduce corneal and scleral shape. This technique is somewhat invasive, due to the physical contact between resin and the eye, and has got known physiological and pharmacological drawbacks.
Known prior studies suggest for example the use of spline curves for approximating a set of corneal measurements, but they are limited to the lens profile and do not consider creation of non-rotation-symmetric geometry. Other studies for asymmetrical geometry design are based on splitting the surface into a number of radially extending segments each approximating the corneal surface. However, even if each segment has a good approximation of the surface, u further effort which is continuous and has continuous first derivatives.